title: Correlation Structure of Fractional Pearson Diffusions.
abstract: The stochastic solution to a diffusion equations with polynomial coefficients is called a Pearson diffusion. If the first time derivative is replaced by a Caputo fractional derivative of order less than one, the stochastic solution is called a fractional Pearson diffusion. This paper develops an explicit formula for the covariance function of a fractional Pearson diffusion in steady state, in terms of Mittag-Leffler functions. That formula shows that fractional Pearson diffusions are long range dependent, with a correlation that falls off like a power law, whose exponent equals the order of the fractional derivative.
authors.affiliation: Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4YH, UK.
authors.forename: Nikolai N
authors.initials: NN
authors.lastname: Leonenko
authors.forename: Mark M
authors.initials: MM
authors.lastname: Meerschaert
authors.forename: Alla
authors.initials: A
authors.lastname: Sikorskii
keywords: Mittag-Leffler function; Pearson diffusion; correlation function; fractional derivative